Question

aaron has been collecting stamps 2 years longer than his sister hannah has been collecting them. as a result, hannah has 40% fewer stamps in her collection than aaron has in his. let a = the number of stamps in aaron’s collection. the expression choose represents the number of stamps hannah has in her collection. the expression choose also represents the number of stamps hannah has in her collection. which expression makes each statement true? click or tap the correct expression from each drop down menu.

Explanation:

Step1: Analyze Hannah's stamps relative to Aaron's

Aaron has \( a \) stamps. Hannah has 40% fewer, so she has \( a - 0.4a = 0.6a \) stamps. This is also \( (1 - 0.4)a \) or \( 60\% \) of \( a \).

Step2: First expression for Hannah's stamps

The number of stamps Hannah has is \( 0.6a \) (or \( a - 0.4a \)), which can be written as \( (1 - 0.4)a \) or \( 0.6a \). So the first expression representing Hannah's stamps is \( 0.6a \) (or equivalent like \( a - 0.4a \)).

Step3: Second expression (stamps Hannah has)

The expression for the number of stamps Hannah has (already found as \( 0.6a \)) also represents her collection. So the second expression is the same as the first, \( 0.6a \) (or \( a - 0.4a \)).

Answer:

First expression (for Hannah's stamps): \( 0.6a \) (or \( a - 0.4a \), \( (1 - 0.4)a \))
Second expression (also Hannah's stamps): \( 0.6a \) (or \( a - 0.4a \), \( (1 - 0.4)a \))